One of my beloved professors told me a story about 30 years ago that has stuck with me, and has informed (not enough, alas) my own teaching practice. He was taking a full-year graduate course in C*-algebras with (I believe) Israel Halperin. By the end of the course they had covered 16 pages (!) of … Read more
A great line from Gretchen Rubin’s delightful blog (The Happiness Project): If you’re not failing, you’re not trying hard enough. It’s similar to a basketball truism about playing defense (“If you commit no fouls at all, you’re not trying hard enough.”), and just as true. She has a book by the same name, which I … Read more
Jian Ghomeshi interviewed Karen Armstrong (her recent book is 12 Steps to a Compassionate Life; for reviews see here, here, and here, for example) yesterday on Q, and she made the point that the major religions have largely failed at training their members to be compassionate, instead emphasizing doctrine, and rigid adherence to rules of … Read more
For four consecutive years I taught a fourth-semester course called “Introduction to Analysis,” in which we looked at differential calculus for a second time, stressing the foundations, the logical structure, and proving all the key theorems. We used Stephen Abbott’s excellent book, Understanding Analysis. The course was intended primarily for math majors, although we had … Read more
Nowadays conic sections are not part of the standard high-school mathematics curriculum in Ontario (at least ellipses and hyperbolas are not; of course circles and parabolas are present), but they are interesting and important curves in mathematics, science, and engineering applications. There are two ways to define an ellipse: (1) as the curve of intersection … Read more
There is one art / no more, no less / to do all things / with artlessness. — Piet Hein The merely poetic destroys poetry. — Vladimir Holan (This post first appeared at my other (now deleted) blog, and was transferred to this blog on 25 January 2021.)
One day a graduate student submitted some writing to me, in which she was explaining rates of change at the high school level. She made an interesting statement: The slope of a secant line joining two points $(a, f(a))$ and $(b, f(b))$ on the graph of a differentiable function $f$ is the average of the … Read more
I believe that the main reason that we procrastinate is that we don’t feel competent. We fear that our results will not be up to some expectation, and the fear paralyzes us. Or rather, in this era with abundant opportunities for diversion, we distract ourselves in wasteful activities so that we don’t have to face … Read more
My parents grew up in a small village in the hills of Calabria, Italy. My Mom used to tell stories about her childhood, which involved getting up insanely early to hike out to work the fields with her father and older brother and sister. They would carry their lunch with them, which often involved only … Read more
I read this while browsing in a store in Ellicottville the other day: An actor included the following provision in his will: When he died he wished to be cremated, and then 10% of his ashes should be thrown in his agent’s face. Funny, eh? It says so much. The Sufis used humorous stories as … Read more